The complete exact solution to the translation-invariant N-body harmonic oscillator problem

Abstract

It is shown that Schrödinger’s nonrelativistic equation for a translation‐invariant system of N particles with arbitrary masses interacting by harmonic pair potentials with arbitrary coupling constants is exactly soluble. An explicit matrix KV is given whose eigenvalues and eigenvectors determine all the exact energies and corresponding eigenfunctions of the N‐particle problem. The result is extended to include systems composed of an arbitrary number of groups of identical particles.